While still in high school, I learned that the tides act as a brake on the Earth, gradually slowing down its rotation, and that the angular momentum lost by the Earth is transferred to the Moon, causing the latter to slowly spiral outwards, away from Earth. I still vividly remember my puzzlement: how — by what mechanism or natural process — did angular momentum get transferred from Earth to the Moon? Just so Newton’s contemporaries must have marveled at his theory of gravity. Newton’s[1] response is well known:

I have not been able to discover the cause of those properties of gravity from phænomena, and I frame no hypotheses…. to us it is enough, that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.

In Newton’s theory, gravitational effects had been simultaneous with their causes. The time-delay between causes and effects in classical electrodynamics and in Einstein’s theory of gravity made it seem possible for a while to explain “how Nature does it.” One only had to transmogrify algorithms that served to calculate effects (having specified their causes) into natural processes by which causes produce effects. This is how the electromagnetic field — a calculational tool — came to be thought of as a physical entity in its own right, which is locally acted upon by charges, which locally acts on charges, and which mediates the action of charges on charges by locally acting on itself.

Today this sleight of hand no longer works.

Classical states are algorithms that assign trivial probabilities to measurement outcomes. Because the probabilities are trivial (either 0 or 1), these states can be re-interpreted as collections of possessed properties and described without reference to “measurement.” Quantum states are algorithms that assign probabilities between 0 and 1, and this is why they cannot be so described. Again, while the classical laws correlate measurement outcomes deterministically (which is why they can be interpreted in causal terms), the quantum-mechanical laws correlate measurement outcomes probabilistically (which is why they can not be so interpreted). In at least one respect, therefore, physics is back to where it was in Newton’s time — and this with a vengeance.

According to Dennis Dieks,[2] Professor of the Foundations and Philosophy of the Natural Sciences at Utrecht University and Editor of Studies in History and Philosophy of Modern Physics,

the outcome of foundational work in the last couple of decades has been that interpretations which try to accommodate classical intuitions are impossible, on the grounds that theories that incorporate such intuitions necessarily lead to empirical predictions which are at variance with the quantum mechanical predictions.

But, seriously, how could anyone have hoped to get away for good with passing off calculational tools — mathematical expressions or equations — as physical entities or natural processes? Was it the hubristic desire to feel “potentially omniscient” — capable in principle of knowing the furniture of the universe and the laws by which this is governed? Or was it the prestige provided by the carefully cultivated image of physicists as having privileged access to Truth?

There is another reason why we cannot hope to explain “how Nature does it.” If quantum mechanics is the fundamental theoretical framework of physics — and while there are a few doubters, nobody has the slightest idea what an alternative framework consistent with the empirical data might look like — then its formalism not only defies reification but also cannot be explained in terms of a “more fundamental” framework. We sometimes speak loosely of a theory as being more fundamental than another but, strictly speaking, “fundamental” has no comparative.

The question we shall be asking ourselves is: what does it take to have stable objects that “occupy space” while being composed of objects that do not “occupy space”? And the answer we shall obtain is: quantum mechanics and special relativity for starters (and thus relativistic quantum mechanics), plus the Stan­dard Model and gen­eral rel­a­tivity, at least as effec­tive the­o­ries.

An approach that rejects the very notion of quantum state evolution, like the one presented here, runs the risk of being dismissed as an ontologically sterile instrumentalism. Yet it is this notion, more than any other, that blocks our view of the ontological implications of quantum mechanics. For instance, whereas the supposition that quantum states evolve leads to the conclusion that the spatiotemporal differentiation of the physical world is complete, one of the ontological implications of quantum mechanics is that the spatiotemporal differentiation of the physical world is incomplete; it does not go “all the way down.”

This is not simply a case of one word against another, for the world’s incomplete spatiotemporal differentiation follows from the manner in which quantum mechanics assigns probabilities, which is testable, whereas the world’s complete spatiotemporal differentiation follows from an assumption about what is the case between measurements, and such an assumption is “not even wrong” in Wolfgang Pauli’s felicitous phrase, inasmuch as it is neither verifiable nor falsifiable.

Again, understanding the central role played by measurements calls for a clear distinction between that which measures and that which is measured. This in turn calls for a rigorous definition of the frequently misused and much maligned word “macroscopic.” But it is precisely the world’s incomplete spatiotemporal differentiation that makes such a definition possible. The central role played by measurements therefore cannot be understood without rejecting the notion that quantum states evolve.

For at least twenty-five centuries, theorists — from metaphysicians to natural philosophers to physicists and philosophers of science — have tried to model reality from the bottom up, starting with an ultimate multiplicity and using concepts of composition and interaction as their basic explanatory tools. If the spatiotemporal differentiation of the physical world is incomplete, then the attempt to understand the world from the bottom up — whether on the basis of an intrinsically and completely differentiated space or spacetime, out of locally instantiated physical properties, or by aggregation, out of a multitude of particles — is doomed to failure. Reality is structured from the top down.

We have seen (or will be seeing) why the well-established laws of physics are just so. They have the particular form that they do because they are preconditions of the possibility of objects that “occupy space” while being composed of objects that do not “occupy space.” The fact that reality is structured from the top down allows us to address a further question: why are stable objects that “occupy space” com­posed of objects that do not “occupy space.”

“The fact that we find ourselves in a quantum world where measurement is possible… will surely involve the same sort of explanation as the fact that we find ourselves in a world where we are able to exist as carbon-based life forms.” — Jeffrey Bub